Mostly depends on what you want to learn, for more Minecraft basics you can either go on Youtube or do a google search on a general Minecraft tutorial.
Afaik, tekkit and bukit are mods. There's a whole seperate mod forum here that you can go and check out.
Any questions whatsoever, you can always send me a PM. =) Specific questions about certain topics are a lot easier to answer, just a general "I need to know more about Minecraft" is hard because it's impossible for anyone else to know what you know and what you still need to learn.
Bukkit is a multiplayer mod which aids in the process of customizing a servers. It is a server-side mod only, so to play on a bukkit server (which if you've played on servers before, chances are you have) you don't need to modify your own game.
Tekkit is both a client and server side mod which allows for greater server customization than bukkit. Tekkit is able to add entirely new blocks to the game. The problem with tekkit is that each player who joins a tekkit server must have tekkit installed in order to play, whereas bukkit allows for plain (vanilla) minecraft.